Problem: Simplify the following expression: $r = \dfrac{2z}{9} + \dfrac{z}{4}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $9$ and $4$ $\lcm(9, 4) = 36$ $ r = \dfrac{4}{4} \cdot \dfrac{2z}{9} + \dfrac{9}{9} \cdot \dfrac{z}{4} $ $r = \dfrac{8z}{36} + \dfrac{9z}{36}$ $r = \dfrac{8z +9z}{36}$ $r = \dfrac{17z}{36}$